Question: Given $ m \angle RPS = 9x + 71$, $ m \angle QPR = 2x + 41$, and $ m \angle QPS = 167$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
Solution: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Substitute in the expressions that were given for each measure: $ {2x + 41} + {9x + 71} = {167}$ Combine like terms: $ 11x + 112 = 167$ Subtract $112$ from both sides: $ 11x = 55$ Divide both sides by $11$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 2({5}) + 41$ Simplify: $ {m\angle QPR = 10 + 41}$ So ${m\angle QPR = 51}$.